In a ripple bed, air is supplied under pressure to two separate air passages in an inflatable mattress. The passages take the form of a series of parallel tubes supplied from common header tubes, one for each passage, located on opposite sides of the mattress. Alternate transverse tubes go to one header tube, and the intervening transverse tube goes to the other header tube. The two passages are inflated and deflated cyclicly, the cycles of the two passages being out of phase so that as one is being inflated the other is being deflated. This creates a ripple effect on the surface of the bed, which has been found particularly useful in helping to prevent bedsores in bed-ridden patients. Leakage of air from the top surface may also be provided to assist in cooling the patient and evaporating moisture. Air beds of this type are for example disclosed in U.S. Pat. Nos. 2,998,817 and 3,653,083 and U.K. Specification No. 949,652.